This project addresses statistical problems generated from collaboration with scientists in other program areas and general statistical problems of current interest. This project is a continuing activity of the Section on Mathematical Statistics and other members of the Branch. Papers have been submitted, are in review or were published in FY 1992 on the following statistical subjects: eigenvalve decompositions of data modeled by multiway arrays; optimal experimental design for data modeled by three-ways arrays; exact likelihood estimation of parameters in a Markov mixture model; computation of determinants of certain large information matrices; Bayesian methods for logistic regression on ill- behaved data; validation methods for screening instruments in surveys of low prevalence disease; national prevalence estimated of disease obtained by adjustment and incorporation of estimates from independent community- based surveys; empirical bayes procedure for examining the relationships among multiple time series; and influence of missing data in randomized clinical trials. Other work in progress includes: methods to improve coverage in surveys; adjustments for covariates in the analysis of categorical data; two-state models for analyzing time series count data; analysis of response surface data with spatial and temporal components; sampling strategies for count data with multiple types of clustering; statistical models and analysis methods for time series of ordinal data; modeling of response surfaces with spatially correlated errors; application of splines to estimate model parameters of multiple correlated response surfaces; modeling effect changes of covariates in the presence of spatial correlation and combining information from negatively correlated nonlinear regressions.